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Question

A steel pipe has a cross-sectional area of 127.20127.20 in 2^2 at 25°F25{\degree} \mathrm{F}. Calculate its crosssectional area when the pipe is heated to 175°F175{\degree} \mathrm{F} .

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Answered 2 years ago
Answered 2 years ago
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Given:\textbf{Given:}

A=127.2 in2A=127.2 \text{ in}^2

T1=25FT_1= 25 ^\circ \text{F}

T2=175FT_2= 175 ^\circ \text{F}

α=6.5×106 F\alpha = 6.5 \times 10^{-6} \text{ } \dfrac{}{^\circ \text{F}}

The change in surface area is given by the formula:

ΔA=2αAΔT\Delta A= 2\cdot \alpha \cdot A \cdot \Delta T

By including the data given in the task we get:

ΔA=2αA(T2T1)=26.5×106127.2(17525)ΔA=0.17 in2\begin{align*} \Delta A&= 2 \cdot \alpha \cdot A \cdot (T_2-T_1)\\ &= 2 \cdot 6.5 \times 10^{-6} \cdot 127.2 \cdot (175-25)\\ &\boxed{\Delta A=0.17 \text{ in}^2 } \end{align*}

To calculate the new area we add the initial value and the area change values:

A2=A+ΔA=127.2+0.17A2=127.37 in2\begin{align*} A_2&=A+\Delta A \\ &=127.2+0.17\\ &\boxed{A_2= 127.37 \text{ in}^2} \end{align*}

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